Synchronization and Control for Directed Multilevel Complex Networks With Arbitrary Couplings
Leijing Xie, Xiwei Liu · International Journal of Robust and Nonlinear Control · 2025
ABSTRACT In this article, we focus on the synchronization problem of directed multilevel complex networks (MLevelN) with arbitrary couplings. First, we propose a new MLevelN model with arbitrarily connected couplings, thus previous fully or partially one‐to‐one connected couplings can be regarded as special cases for this model. Then, using the normalized left eigenvector of couplings, criteria on two typical types of synchronization for MLevelN are obtained. Besides, we consider MLevelN with disconnected layers, and by using Tarjan's algorithm, it can be rearranged to MLevelN with different number of nodes in different layers. Furthermore, different control strategies for the rearranged MLevelN are also designed, and pinning only one node (arbitrarily chosen) can make the whole MLevelN realize complete synchronization. Then, the results are applied on a three‐level reaction‐diffusion neural network as an application. Finally, the effectiveness of the obtained criteria is verified by numerical simulations.